Fast intersection of two sorted integer arrays

Question

I need to find the intersection of two sorted integer arrays and do it very fast.

Right now, I am using the following code:

int i = 0, j = 0;

while (i          


        

Answer 1

Yorye Nathan gave me the fastest intersection of two arrays with the last "unsafe code" method. Unfortunately it was still too slow for me, I needed to make combinations of array intersections, which goes up to 2^32 combinations, pretty much no? I made following modifications and adjustments and time dropped to 2.6X time faster. You need to make some pre optimization before, for sure you can do it some way or another. I am using only indexes instead the actual objects or ids or some other abstract comparison. So, by example if you have to intersect big number like this

Arr1: 103344, 234566, 789900, 1947890, Arr2: 150034, 234566, 845465, 23849854

put everything into and array

Arr1: 103344, 234566, 789900, 1947890, 150034, 845465,23849854

and use, for intersection, the ordered indexes of the result array

Arr1Index: 0, 1, 2, 3 Arr2Index: 1, 4, 5, 6

Now we have smaller numbers with whom we can build some other nice arrays. What I did after taking the method from Yorye, I took Arr2Index and expand it into, theoretically boolean array, practically into byte arrays, because of the memory size implication, to following:

Arr2IndexCheck: 0, 1, 0, 0, 1, 1 ,1

that is more or less a dictionary which tells me for any index if second array contains it. The next step I did not use memory allocation which also took time, instead I pre-created the result array before calling the method, so during the process of finding my combinations I never instantiate anything. Of course you have to deal with the length of this array separately, so maybe you need to store it somewhere.

Finally the code looks like this:

    public static unsafe int IntersectSorted2(int[] arr1, byte[] arr2Check, int[] result)
    {
        int length;

        fixed (int* pArr1 = arr1, pResult = result)
        fixed (byte* pArr2Check = arr2Check)
        {
            int* maxArr1Adr = pArr1 + arr1.Length;
            int* arr1Value = pArr1;
            int* resultValue = pResult;

            while (arr1Value < maxArr1Adr)
            {
                if (*(pArr2Check + *arr1Value) == 1)
                {
                    *resultValue = *arr1Value;
                    resultValue++;
                }

                arr1Value++;
            }

            length = (int)(resultValue - pResult);
        }

        return length;
    }

You can see the result array size is returned by the function, then you do what you wish(resize it, keep it). Obviously the result array has to have at least the minimum size of arr1 and arr2.

The big improvement, is that I only iterate through the first array, which would be best to have less size than the second one, so you have less iterations. Less iterations means less CPU cycles right?

So here is the really fast intersection of two ordered arrays, that if you need a reaaaaalllyy high performance ;).

Answer 2

Have you tried something simple like this:

var a = Enumerable.Range(1, int.MaxValue/100).ToList();
var b = Enumerable.Range(50, int.MaxValue/100 - 50).ToList();

//var c = a.Intersect(b).ToList();
List<int> c = new List<int>();

var t1 = DateTime.Now;

foreach (var item in a)
{
    if (b.BinarySearch(item) >= 0)
        c.Add(item);
}

var t2 = DateTime.Now;

var tres = t2 - t1;

This piece of code takes 1 array of 21,474,836 elements and the other one with 21,474,786

If I use var c = a.Intersect(b).ToList(); I get an OutOfMemoryException

The result product would be 461,167,507,485,096 iterations using nested foreach

But with this simple code, the intersection occurred in TotalSeconds = 7.3960529 (using one core)

Now I am still not happy, so I am trying to increase the performance by breaking this in parallel, as soon as I finish I will post it

Answer 3

UPDATE

The fastest I got was 200ms with arrays size 10mil, with the unsafe version (Last piece of code).

The test I've did:

var arr1 = new int[10000000];
var arr2 = new int[10000000];

for (var i = 0; i < 10000000; i++)
{
    arr1[i] = i;
    arr2[i] = i * 2;
}

var sw = Stopwatch.StartNew();

var result = arr1.IntersectSorted(arr2);

sw.Stop();

Console.WriteLine(sw.Elapsed); // 00:00:00.1926156

Full Post:

I've tested various ways to do it and found this to be very good:

public static List<int> IntersectSorted(this int[] source, int[] target)
{
    // Set initial capacity to a "full-intersection" size
    // This prevents multiple re-allocations
    var ints = new List<int>(Math.Min(source.Length, target.Length));

    var i = 0;
    var j = 0;

    while (i < source.Length && j < target.Length)
    {
        // Compare only once and let compiler optimize the switch-case
        switch (source[i].CompareTo(target[j]))
        {
            case -1:
                i++;

                // Saves us a JMP instruction
                continue;
            case 1:
                j++;

                // Saves us a JMP instruction
                continue;
            default:
                ints.Add(source[i++]);
                j++;

                // Saves us a JMP instruction
                continue;
        }
    }

    // Free unused memory (sets capacity to actual count)
    ints.TrimExcess();

    return ints;
}

For further improvement you can remove the ints.TrimExcess();, which will also make a nice difference, but you should think if you're going to need that memory.

Also, if you know that you might break loops that use the intersections, and you don't have to have the results as an array/list, you should change the implementation to an iterator:

public static IEnumerable<int> IntersectSorted(this int[] source, int[] target)
{
    var i = 0;
    var j = 0;

    while (i < source.Length && j < target.Length)
    {
        // Compare only once and let compiler optimize the switch-case
        switch (source[i].CompareTo(target[j]))
        {
            case -1:
                i++;

                // Saves us a JMP instruction
                continue;
            case 1:
                j++;

                // Saves us a JMP instruction
                continue;
            default:
                yield return source[i++];
                j++;

                // Saves us a JMP instruction
                continue;
        }
    }
}

Another improvement is to use unsafe code:

public static unsafe List<int> IntersectSorted(this int[] source, int[] target)
{
    var ints = new List<int>(Math.Min(source.Length, target.Length));

    fixed (int* ptSrc = source)
    {
        var maxSrcAdr = ptSrc + source.Length;

        fixed (int* ptTar = target)
        {
            var maxTarAdr = ptTar + target.Length;

            var currSrc = ptSrc;
            var currTar = ptTar;

            while (currSrc < maxSrcAdr && currTar < maxTarAdr)
            {
                switch ((*currSrc).CompareTo(*currTar))
                {
                    case -1:
                        currSrc++;
                        continue;
                    case 1:
                        currTar++;
                        continue;
                    default:
                        ints.Add(*currSrc);
                        currSrc++;
                        currTar++;
                        continue;
                }
            }
        }
    }

    ints.TrimExcess();
    return ints;
}

In summary, the most major performance hit was in the if-else's. Turning it into a switch-case made a huge difference (about 2 times faster).

Answer 4

C# doesn't support SIMD. Additionally, and I haven't yet figured out why, DLL's that use SSE aren't any faster when called from C# than the non-SSE equivalent functions. Also, all SIMD extensions that I know of don't work with branching anyway, ie your "if" statements.

If you're using .net 4.0, you can use Parallel For to gain speed if you have multiple cores. Otherwise you can write a multithreaded version if you have .net 3.5 or less.

Here is a method similar to yours:

    IList<int> intersect(int[] arr1, int[] arr2)
    {
        IList<int> intersect = new List<int>();
        int i = 0, j = 0;
        int iMax = arr1.Length - 1, jMax = arr2.Length - 1;
        while (i < iMax && j < jMax)
        {
            while (i < iMax && arr1[i] < arr2[j]) i++;
            if (arr1[i] == arr2[j]) intersect.Add(arr1[i]);
            while (i < iMax && arr1[i] == arr2[j]) i++; //prevent reduntant entries
            while (j < jMax && arr2[j] < arr1[i]) j++;
            if (arr1[i] == arr2[j]) intersect.Add(arr1[i]);
            while (j < jMax && arr2[j] == arr1[i]) j++; //prevent redundant entries
        }
        return intersect;
    }

This one also prevents any entry from appearing twice. With 2 sorted arrays both of size 10 million, it completed in about a second. The compiler is supposed to remove array bounds checks if you use array.Length in a For statement, I don't know if that works in a while statement though.

Answer 5

Are arrCollection1 and arrCollection2 collections of arrays of integers? IN this case you should get some notable improvement by starting second loop from i+1 as opposed to 0